Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------------ | 
 | Output Created                               | 22-APR-2002 18:39:26                                   | 
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 | Comments                                     |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav          | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Filter                         | WLA                                                    | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Weight                         | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Split File                     | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | N of Rows in Working Data File | 70                                                     | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 GSD=.5 EMIN=0 EMAX=3 .              | 
 |                                              | COMPUTE PRED_ =                                        | 
 |                                              | emin+(emax-emin)*(CDF.NORMAL(lg10(dose),ed,gsd)).      | 
 |                                              | CNLR toothdef                                          | 
 |                                              | /OUTFILE='C:\TEMP\spss158\SPSSFNLR.TMP'                | 
 |                                              | /PRED PRED_                                            | 
 |                                              | /BOUNDS ED <= 4; ED >= -2; GSD <= 1.699; GSD >= .01;   | 
 |                                              | EMIN = 0; EMAX = 3                                     | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .                    | 
 |                                              |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.03                                             | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED         GSD        EMIN        EMAX

     0.2    64.16280078  1.00000000  .500000000  .000000000  3.00000000
     1.1    51.26516426  1.63574815  .754087343  .000000000  3.00000000
     2.1    45.55414297  1.08327998  1.69900000  .000000000  3.00000000
     3.1    44.53703326  1.27529253  1.69900000  .000000000  3.00000000
     4.1    44.47547812  1.33582158  1.69900000  .000000000  3.00000000
     5.1    44.47547597  1.33546598  1.69900000  .000000000  3.00000000
     6.1    44.47547597  1.33546613  1.69900000  .000000000  3.00000000

Run stopped after 6 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4      163.02452       40.75613
  Residual               66       44.47548         .67387
  Uncorrected Total      70      207.50000

  (Corrected Total)      69       89.20000

  R squared = 1 - Residual SS / Corrected SS =     .50140

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED         1.335466129   .727441552  -.116917790  2.787850049
  GSD        1.699000000  1.081777725  -.460838916  3.858838916
  EMIN        .000000000   .430554724  -.859630243   .859630243
  EMAX       3.000000000   .967096258  1.069130021  4.930869979

  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED       GSD      EMIN      EMAX

  ED          1.0000     .6178    -.1518     .8527
  GSD          .6178    1.0000    -.8102     .8978
  EMIN        -.1518    -.8102    1.0000    -.5978
  EMAX         .8527     .8978    -.5978    1.0000

